TY - JOUR
T1 - On the Dynamics of the Tavis-Cummings Model
AU - Dong, Zhiyuan
AU - Zhang, Guofeng
AU - Wu, Ai Guo
AU - Wu, Re Bing
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China under Grant 6217023269, Grant 62003111, Grant 61833010, and Grant 62173201, in part by the Hong Kong Research Grant Council under Grant 15208418 and Grant 15203619, in part by the Shenzhen Fundamental Research Fund, China under Grant JCYJ20190813165207290, and in part by the Natural Science Foundation of Guangdong Province under Grant 2022A1515010390.
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2023/4/1
Y1 - 2023/4/1
N2 - The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.
AB - The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.
KW - Open quantum systems
KW - Tavis-Cummings model
KW - quantum control
KW - two-level systems (TLSs)
UR - https://www.scopus.com/pages/publications/85129658976
U2 - 10.1109/TAC.2022.3169582
DO - 10.1109/TAC.2022.3169582
M3 - Journal article
AN - SCOPUS:85129658976
SN - 0018-9286
VL - 68
SP - 2048
EP - 2063
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
ER -